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    <title>hank</title>
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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>hank</b> -  covariance to hankel matrix</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>[hk]=hank(m,n,cov)  </tt>
      </dd>
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    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>m</b>
        </tt>: number of bloc-rows</li>
      <li>
        <tt>
          <b>n</b>
        </tt>: number of bloc-columns</li>
      <li>
        <tt>
          <b>cov</b>
        </tt>: sequence of covariances; it must be given as :[R0 R1 R2...Rk]</li>
      <li>
        <tt>
          <b>hk</b>
        </tt>: computed hankel matrix</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    this function builds the hankel matrix of size <tt>
        <b>(m*d,n*d)</b>
      </tt>
    from the covariance sequence of a vector process</p>
    <h3>
      <font color="blue">Examples</font>
    </h3>
    <pre>

//Example of how to use the hank macro for 
//building a Hankel matrix from multidimensional 
//data (covariance or Markov parameters e.g.)
//
//This is used e.g. in the solution of normal equations
//by classical identification methods (Instrumental Variables e.g.)
//
//1)let's generate the multidimensional data under the form :
//  C=[c_0 c_1 c_2 .... c_n]
//where each bloc c_k is a d-dimensional matrix (e.g. the k-th correlation 
//of a d-dimensional stochastic process X(t) [c_k = E(X(t) X'(t+k)], ' 
//being the transposition in scilab)
//
//we take here d=2 and n=64
//
c=rand(2,2*64)
//
//generate the hankel matrix H (with 4 bloc-rows and 5 bloc-columns)
//from the data in c
//
H=hank(4,5,c);
//
 
  </pre>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="../elementary/toeplitz.htm">
        <tt>
          <b>toeplitz</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
    <h3>
      <font color="blue">Author</font>
    </h3>
    <p>G. Le Vey</p>
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